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added schaffer2 function

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added output for improvement of fitness
added CMAES algorithm, that requires further testing
This commit is contained in:
Daniel Lukats
2019-09-23 14:11:46 +02:00
parent 93e9234ce6
commit 14c7756802
4 changed files with 97 additions and 42 deletions
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18
functions.py
View File

@@ -17,17 +17,29 @@ class Function:
X, Y = np.meshgrid(x, y)
return x, y, self.eval(X, Y)
class Rastrigin(Function):
def __init__(self, A: int = 10):
super().__init__(
xlim=(-5.12, 5.12),
ylim=(-5.12, 5.12),
xlim=(-6.12, 6.12),
ylim=(-6.12, 6.12),
minimum=(0, 0),
eval=lambda x, y: self.A * 2 + \
(x**2 - self.A * np.cos(2 * np.pi * x)) + \
(y**2 - self.A * np.cos(2 * np.pi * y)))
self.A = A
class Schaffer2(Function):
def __init__(self):
super().__init__(
xlim=(-50, 50),
ylim=(-50, 50),
minimum=(0, 0),
eval=lambda x, y: 0.5 + \
(np.sin(x**2 - y**2)**2 - 0.5) / \
((1 + 0.001 * (x**2 + y**2))**2))
class Sphere(Function):
def __init__(self):
super().__init__(

43
main.py Normal file
View File

@@ -0,0 +1,43 @@
import functions
import numpy as np
import solvers
from matplotlib import pyplot as plt
def main():
plot_rest = True
f = functions.Rastrigin()
# f = functions.Sphere()
# s = solvers.SimpleEvolutionStrategy(f, np.array([2, 2]))
s = solvers.CMAEvolutionStrategy(f, np.array([2.0, 2.0]), np.array([[2.0, 0.0], [0.0, 2.0]]))
old_fitness = 100
fitness = old_fitness * 0.9
old = None
plt.set_cmap('Spectral')
while abs(old_fitness - fitness) > 0.001:
old_fitness = fitness
samples = s.sample(2000)
elite, fitness = s.rank(samples, 150)
s.update(elite)
if plot_rest:
rest = np.setdiff1d(samples, elite, assume_unique=True)
rest = rest.reshape((int(rest.shape[0]/2), 2))
plt.pcolormesh(*f.grid())
if plot_rest:
plt.scatter(*rest.transpose(), color="dimgrey")
if old is not None:
plt.scatter(*old.transpose(), color="orange")
plt.scatter(*elite.transpose(), color="yellow")
# plt.scatter(*elite[0].transpose(), color="green")
print('old fitness: {}\nnew fitness: {}\nimprovement: {}\n'.format(old_fitness, fitness,
old_fitness - fitness))
plt.show()
old = elite
if __name__ == '__main__':
main()

43
solvers.py
View File

@@ -10,7 +10,7 @@ class Solver(ABC):
self.function = function
@abstractmethod
def rank(self, samples: Iterable[Iterable[float]], elite_size: int) -> (Iterable[Tuple], Iterable[Tuple], float):
def rank(self, samples: Iterable[Iterable[float]], elite_size: int) -> (Iterable[Iterable[float]], float):
pass
@abstractmethod
@@ -18,7 +18,7 @@ class Solver(ABC):
pass
@abstractmethod
def update(elite: Iterable[Tuple]):
def update(elite: Iterable[Iterable[float]]):
pass
@@ -33,7 +33,7 @@ class SimpleEvolutionStrategy(Solver):
else:
self.sigma = [1] * len(mu)
def rank(self, samples: Iterable[Iterable[float]], elite_size: int) -> (Iterable[Tuple], Iterable[float]):
def rank(self, samples: Iterable[Iterable[float]], elite_size: int) -> (Iterable[Iterable[float]], Iterable[float]):
fitness = self.function.eval(*samples.transpose())
samples = samples[np.argsort(fitness)]
fitness = np.sort(fitness)
@@ -43,6 +43,41 @@ class SimpleEvolutionStrategy(Solver):
def sample(self, n: int) -> Iterable[Iterable[float]]:
return np.array([np.random.multivariate_normal(self.mu, np.diag(self.sigma)) for _ in range(n)])
def update(self, elite: Iterable[Tuple]):
def update(self, elite: Iterable[Iterable[float]]):
self.mu = elite[0]
class CMAEvolutionStrategy(Solver):
def __init__(self, function: Function, mu: Iterable[float], covariances: Iterable[float] = None):
if covariances is not None and len(mu) != covariances.shape[0] and len(mu) != covariances.shape[1]:
raise Exception('Length of mu and covariance matrix must match')
super().__init__(function)
self.mu = mu
if covariances is not None:
self.covariances = covariances
else:
self.covariances = np.array([[1.0, 0.0], [0.0, 1.0]])
def rank(self, samples: Iterable[Iterable[float]], elite_size: int) -> (Iterable[Iterable[float]], Iterable[float]):
fitness = self.function.eval(*samples.transpose())
samples = samples[np.argsort(fitness)]
fitness = np.sort(fitness)
elite = samples[0:elite_size]
return elite, fitness[0]
def sample(self, n: int) -> Iterable[Iterable[float]]:
return np.array([np.random.multivariate_normal(self.mu, self.covariances) for _ in range(n)])
def update(self, elite: Iterable[Iterable[float]]):
mu = self.mu
x = elite.transpose()[0]
y = elite.transpose()[1]
self.mu[0] = np.average(x)
self.mu[1] = np.average(y)
# TODO fix covariance matrix calculation using the tutorial by Nikolaus Hansen
self.covariances[0][0] = np.average((x - mu[0])**2)
self.covariances[1][1] = np.average((y - mu[1])**2)
self.covariances[0][1] = np.average((x - mu[0]) * (y - mu[1]))
# self.covariances = np.cov(elite.transpose())

35
test.py
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@@ -1,35 +0,0 @@
import functions
import numpy as np
import solvers
from matplotlib import pyplot as plt
plot_rest = True
f = functions.Rastrigin()
# f = functions.Sphere()
s = solvers.SimpleEvolutionStrategy(f, np.array([2, 2]))
old_fitness = 100
fitness = old_fitness * 0.9
old = None
plt.plasma()
while abs(old_fitness - fitness) > 0.001:
old_fitness = fitness
samples = s.sample(100)
elite, fitness = s.rank(samples, 10)
s.update(elite)
if plot_rest:
rest = np.setdiff1d(samples, elite, assume_unique=True)
rest = rest.reshape((int(rest.shape[0]/2), 2))
plt.pcolormesh(*f.grid())
if plot_rest:
plt.scatter(*rest.transpose(), color="dimgrey")
if old is not None:
plt.scatter(*old.transpose(), color="lightgrey")
plt.scatter(*elite.transpose(), color="yellow")
plt.scatter(*elite[0].transpose(), color="green")
plt.show()
old = elite